Exponential stability for uncertain neutral systems with Markov jumps

This paper deals with the global exponential stability problems for stochastic neutral Markov jump systems (MJSs) with uncertain parameters and multiple time-delays. The delays are respectively considered as constant and time varying cases, and the uncertainties are assumed to be norm bounded. By selecting appropriate Lyapunov-Krasovskii functions, it gives the sufficient condition such that the uncertain neutral MJSs are globally exponentially stochastically stable for all admissible uncertainties. The stability criteria are formulated in the form of linear matrix inequalities (LMIs), which can be easily checked in practice. Finally, two numerical examples are exploited to illustrate the effectiveness of the developed techniques.

[1]  D. Sworder,et al.  Feedback control of a class of linear discrete systems with jump parameters and quadratic cost criteria , 1975 .

[2]  R. Rogers,et al.  An LQ-solution to a control problem associated with a solar thermal central receiver , 1983 .

[3]  Michael Athans,et al.  Command and control (C2) theory: A challenge to control science , 1986 .

[4]  H. Chizeck,et al.  Controllability, stabilizability, and continuous-time Markovian jump linear quadratic control , 1990 .

[5]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[6]  Lihua Xie,et al.  Robust control of a class of uncertain nonlinear systems , 1992 .

[7]  M. Fragoso,et al.  Stability Results for Discrete-Time Linear Systems with Markovian Jumping Parameters , 1993 .

[8]  Stephen P. Boyd,et al.  Linear Matrix Inequalities in Systems and Control Theory , 1994 .

[9]  Y. Bar-Shalom,et al.  Stabilization of jump linear gaussian systems without mode observations , 1996 .

[10]  El-Kébir Boukas,et al.  Stochastic stability and guaranteed cost control of discrete-time uncertain systems with Markovian jumping parameters , 1997 .

[11]  E. Boukas,et al.  Mean square stochastic stability of linear time-delay system with Markovian jumping parameters , 1998, IEEE Trans. Autom. Control..

[12]  A. Bellen,et al.  Methods for linear systems of circuit delay differential equations of neutral type , 1999 .

[13]  Hailiang Yang,et al.  Technical Communique: Exponential stabilizability of stochastic systems with Markovian jumping parameters> >>altfn>This paper was not presented at any IFAC meeting. This paper was recommended for publication in revised form by Editor Peter Dorato. , 1999 .

[14]  Vincent D. Blondel,et al.  Proceedings of the 2000 American Control Conference , 2000, Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334).

[15]  Sangchul Won,et al.  Stability analysis for neutral delay-differential systems , 2000, J. Frankl. Inst..

[16]  Emilia Fridman,et al.  New Lyapunov-Krasovskii functionals for stability of linear retarded and neutral type systems , 2001, Syst. Control. Lett..

[17]  Xuerong Mao,et al.  Exponential stability of stochastic delay interval systems with Markovian switching , 2002, IEEE Trans. Autom. Control..

[18]  Ju H. Park,et al.  Simple criterion for asymptotic stability of interval neutral delay-differential systems , 2003, Appl. Math. Lett..

[19]  Xingfu Zou,et al.  Stability of linear neutral systems with multiple delays: boundary criteria , 2004, Appl. Math. Comput..

[20]  Dong Yue,et al.  A delay-dependent stability criterion of neutral systems and its application to a partial element equivalent circuit model , 2004 .

[21]  M. Fragoso,et al.  Mean Square Stabilizability of Continuous-Time Linear Systems with Partial Information on the Markovian Jumping Parameters , 2004 .

[22]  James Lam,et al.  On robust stabilization of Markovian jump systems with uncertain switching probabilities , 2005, Autom..

[23]  Liu Meiqin.  Stability analysis of neutral-type nonlinear delayed systems: An LMI approach * , 2006 .

[24]  Geir E. Dullerud,et al.  A stability and contractiveness analysis of discrete-time Markovian jump linear systems , 2007, Autom..

[25]  MingZhu Liu,et al.  Stability Criteria of Linear Neutral Systems With Multiple Delays , 2007, IEEE Transactions on Automatic Control.

[26]  P. Shi,et al.  Robust stability criteria for uncertain neutral system with time delay and nonlinear uncertainties , 2008 .